On strong pseudo-amenability of some Banach algebras

Abstract

In this paper, we introduce a new notion of strong pseudo-amenability for Banach algebras. We study strong pseudo-amenability of some matrix algebras. Using this tool, we characterize strong pseudo-amenability of [Formula: see text], provided that [Formula: see text] is a uniformly locally finite inverse semigroup. As an application, we show that for a Brandt semigroup [Formula: see text], [Formula: see text] is strong pseudo-amenable if and only if [Formula: see text] is amenable and [Formula: see text] is finite. We give some examples to show the differences between strong pseudo-amenability and the other classical notions of amenability.